Picking up flying is usually easy. Dropping trips is allowed as long as there is adequate reserve coverage. If there is not you can still put the trip into open time for other pilots to pick up subject to FAR’s and the contract. You can also post the trip on the pilot swap board where pilots can take the trip subject only to FAR’s. Once a year you get a authorized personal leave drop where reserve coverage need only be 25% of required. You also can split off a vacation day to drop a trip twice a year subject to the same 25% of coverage rules so in effect you have 3 priority drops a year.
The second option is to swap the trips. Swaps can be done via the company scheduling system (DBMS) where the swap if the dropped trip is above adequate coverage is approved subject to FAR’s. If the trip is below Adequate coverage it will still be approved as long as the trip you are swapping for has the same or worse coverage.
Picking up trips generally falls into two categories. You can pick up at straight rates (white slip) subject to FAR’s and contractual limits. You can also put in a request (greenslip) to pick up at double pay subject only to FAR’s. How the company assigns trips is governed in section 23 of the contract via a assignment ladder. It’s long and complex but the short cliff note version is the company covers unassigned trips with legal reserves, white slips and then green slips.
There are other graduate level methods to force trip drops such as white slipping a trip in the current month forcing a FAR drop in the following month. Swapping trips in one month for another month ect.. You need a guru and the Scheduling reference handbook to understand it all.